This paper proposes novel distributed control schemes for large-scale deployment of flexible demand. The problem of efficiently coordinating price-responsive appliances operating in the electricity market is tackled within a game-theoretical framework. Adopting the concept of Nash equilibrium and Lyapunov-based techniques, a new iterative control algorithm is designed in order to always converge to a satisfactory solution for the individual customers, which aim at minimizing their energy costs. From the system perspective, it is shown that global quantities such as total generation costs are reduced at each algorithm iteration. These results are achieved for any penetration level of flexible demand and for all types of interruptible electrical appliances. The proposed control scheme can be applied in practice through a one-shot implementation that, at the price of a negligible degradation of the equilibrium performance, ensures faster convergence to a stable solution. Simulation results are also presented, testing the novel schemes in realistic future scenarios of the Great Britain power system with high penetration of flexible demand.